What physical tools (lenses/filters/etc) can be used to blur a part of an image whilst taking the photo. (I don't mean software filters in post-processing, and I want to blur selective areas specifically for creative effect, rather than only using true depth of field.)

For example, portrait of person in front of a wall: wall is perpendicular to camera, so is evenly slightly out of focus due to depth of field. But I want an area of the wall along the top to be much more blurred, but with a natural lens effect rather than smooth software blur.

3 Answers
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Tilting the lens can be used to blur part of an image in a way similar to how you describe. A special lens (tilt-shift) or adaptor is required to be able to do this. With some lenses you can get away with detaching the lens and holding it at an angle, a technique known as freelensing.

This will add a gradual blur to a perpendicular wall very similar to the effects of decreased DOF (so similar in fact that this technique is used to produce "fake miniatures", images of life sized objects made to appear microscopic by simulating very shallow depth of field.

An alternative is to use something like vaseline on the front of the lens (or preferably on a filter mounted on the lens). This gives a classic soft focus type blur, very different in character to out-of-focus blur.

There are a number of different kinds of filters to do this, usually soft focus or diffusion filters that provide a fuzzy edge while leaving a clear center or some variation there of.

However, you don't have to buy special filters if you're willing to mess up something like a cheaper UV filter for a bit (you can clean it after). Basically, if you smear a little Vaseline around the edge of the filter, leaving the center clear, you can achieve the same effects. Pantyhose over the lens is another way to soften, though it's tricky to get a clear center there.

Your other approach might be to get a Lee or Cokin filter holder and build a filter. A 1 mm thick cardboard stock with an opening that you cover with transparencies that have been marked up to blur (sandpaper might be useful there) would be an approach. To be honest, I just thought of this one as I did something like it for DIY shaped bokeh once, so I think it would be quite easy and very re-usable without making a mess of a UV filter...

The advantage, by the way, of the DIY options is that you can control the size and shape of the blur.

One way to do this is by tilting the lens. This causes the plane of focus to not correspond with the flat plane of the sensor, letting you change where the blur falls. You can buy specialized tilt-shift lenses, which are usually rather expensive and large, or you can try "freelensing", but I think the best combination of ease of use and budget is the series of lenses from Lensbaby.

These are designed to bend to provide exactly the effect you are looking for. Their cheaper designs, like the Spark and Muse are designed to be free-flowing and in-the-moment, and somewhat difficult to use in a repeatable way. The more expensive Composer models are designed with greater precision in mind (but aren't necessarily in inherently "better").

Each of these can take a variety of swappable optics, from all-plastic (or glass) single-element lenses up through the more multi-element, multi-coated "Sweet 35" design.

If this kind of effect is of interest to you, and you don't want the expense (or size and weight, or the need for careful adjustment for each shot), and you're interested in doing it in-camera rather than faking it in post-production, to me Lensbaby is the best answer.